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Beliebt Funktionen >

extreme f(x)=1+x^2e^{5-3x}

Lösung

extrempunkte

f (x) = 1 + x^{2} e^{5 - 3 x}

Lösung

Minimum (0, 1), Maximum (\frac{2}{3}, 1 + \frac{4 e ^{3}}{9})

Schritte zur Lösung

f^{'} (x) = - e^{- 3 x + 5} x (3 x - 2)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{2}{3},

Absteigend

: \frac{2}{3} < x < \infty

Stecke

x = 0

in

1 + x^{2} e^{5 - 3 x} : 1

Minimum (0, 1)

Stecke

x = \frac{2}{3}

in

1 + x^{2} e^{5 - 3 x} : 1 + \frac{4 e ^{3}}{9}

Maximum (\frac{2}{3}, 1 + \frac{4 e ^{3}}{9})

Minimum (0, 1), Maximum (\frac{2}{3}, 1 + \frac{4 e ^{3}}{9})

Graph

Beliebte Beispiele

extreme y=-4e^{-4t}+5e^{-5t}

e x t re m e y = - 4 e^{- 4 t} + 5 e^{- 5 t}

extreme f(x,y)=e^{1-y^2}-(x^2+xy)

e x t re m e f (x, y) = e^{1 - y^{2}} - (x^{2} + x y)

extreme (x^2-2x+4)/(x-2)

e x t re m e \frac{x ^{2} - 2 x + 4}{x - 2}

extreme f(x,y)=x^2+y^2=8

e x t re m e f (x, y) = x^{2} + y^{2} = 8

extreme f(x/y)=xsqrt(y)+ysqrt(x)

e x t re m e f (\frac{x}{y}) = x y + y x